symbolically solve an integral of ArcSinh[..]

*To*: mathgroup at smc.vnet.net*Subject*: [mg7809] symbolically solve an integral of ArcSinh[..]*From*: pknaus at psap73.cern.ch (Patrick KNAUS)*Date*: Sat, 12 Jul 1997 02:45:51 -0400*Organization*: CERN, European Laboratory for Particle Physics*Sender*: owner-wri-mathgroup at wolfram.com

Hello, could you please help me with the following problem: I try to integrate symbolically Integrate[ArcSinh[(a-Sqrt[b^2-x^2])/(c-x)],x] where a,b,c=const but don't obtain any solution using Mathematica 2.2 and 3.0. I tried some equivalent formulations of the integrand like ArcSinh[z]=Log[z-Sqrt[1+z^2] ArcSinh[z]=-I ArcSin[I z] where z is the argument of ArcSinh in the integral: without success. Are there any tricks you could suggest me to try out, any nice substitution? I suspect the solution to contain some elliptic integrals. best wishes, Patrick -- ----- From: Patrick Knaus To: mathgroup at smc.vnet.net CERN, Division PS Email: Patrick.Knaus at cern.ch CH-1211 Geneva 23 Tel: +41-22-767.2593